Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsRefraction at curved surface/LensEasy2 minPYQ_2020

PhysicsEasysingle choice

One plano-convex and one plano-concave lens of the same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $μ_{1}$ and that of $2$ is $μ_{2}$ , then the focal length of the combination is:

Options:

Answer:

Solution:

From lens maker’s formula,
$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$\frac{1}{f_{1}} = (μ_{1} - 1) (\frac{1}{\infty} - \frac{1}{(- R)}) = \frac{μ_{1} - 1}{R}$
$\frac{1}{f_{2}} = (μ_{2} - 1) (\frac{1}{(- R)} - \frac{1}{\infty}) = - \frac{(μ_{2} - 1)}{R}$
$\frac{1}{f_{e q}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} = \frac{μ_{1} - 1}{R} - \frac{μ_{2} - 1}{R}$
$= \frac{μ_{1} - μ_{2}}{R}$
$f_{e q} = \frac{R}{μ_{1} - μ_{2}}$

Subject:PhysicsTopic:Geometrical OpticsSubtopic:Refraction at curved surface/Lens

⏱ 2mℹ️ Source: PYQ_2020

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